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Tickets will go on general sale at 11am on Friday, February 14.
The groups revealed their tour plans in a series of tweets by posting both the New Zealand and Australian flags this week.
The groups will begin their "Hella Mega Tour" on June 13 in France, before touring the rest of Europe and America.
Special guest at both New Zealand concerts will be New Zealand guitar pop band The Beths.
Green Day’s 1994 breakout album Dookie had been widely credited with popularising and reviving mainstream interest in punk rock.
In 2004, it released the rock opera American Idiot which took home the Grammy Award for Best Rock Album.
Fall Out Boy’s debut album Take This to Your Grave has been cited as an influential blueprint for pop punk music in the 2000s, while Weezer’s 14th studio album is due out out in May this year.
Its catalogue includes hits Buddy Holly, Undone (The Sweater Song), Say It Ain’t So and El Scorcho.